Find the greatest common factor of $14$ and $55$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $14$ and $55$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}14 &=2\cdot7\\\\\\\\ 55&=5\cdot11 \end{aligned}$ Since these numbers have no common prime factors, we say that the GCF is $1$. This is because all numbers share a factor of $1$ : $ \begin{aligned}14 &=2\cdot7\cdot1\\\\\\\\ 55&=5\cdot11\cdot1 \end{aligned}$ The greatest common factor of $14$ and $55$ is $1$.